The MXDF data were obtained as a part of the MUSE guaranteed time observations (GTO) program (PI: R. Bacon). The survey design of MXDF is presented in Bacon et al. in prep. [1]}. The field has a circular shape, centered at R.A.=53.\(^{\circ }\) 16467 and DEC.=-27.\(^{\circ }\) 78537 (J2000 FK5) with a radius of \(r=44\)  arcsec (1.7 arcmin\(^2\) ), and is located inside the Hubble eXtreme Deep Field [2]} with deep Hubble Space Telescope (HST) data. It is also covered by the MUSE-Hubble Ultra Deep Field (HUDF) with 10- to 30-hour MUSE integration in a 9 arcmin\(^2\)  area [3]}. The MXDF is the deepest MUSE survey with AO, reaching up to 140 hours at \(r\lesssim 29\)  arcsec and 100 hours out to \(r=31\)  arcsec, while the outer edge has a 10-hour integration (\(r\lesssim 41\)  arcsec). In this paper we use the very deep area with 100-to 140-hour integration, located inside a radius of 31 arcsec from the center of the field [1]}, which we used in this paper. The corresponding survey volume in this work is \(4.0\times 10^3\)  cMpc\(^3\)  (\(z=2.86\) –\(4.44\) , excluding an AO gap, see below for more details).
